If I turn my head to one side, I find I can actually breathe through the seaweed. And as I inhale, hot fleshy fronds fall into my mouth. At first I was wary of them. Now, I've started to nibble the fronds. In fact, I can't resist them: they taste and feel like salty pencil erasers with an inner layer of softened fingernail. Bizarrely delicious. With a warm complex smell, like damp dog and hops.

Hot seaweed is piled all over my body and my head, and through the steamy haze I can just make out the figure of my middle son, Rex, who's 15. He looks like a Dalek. His body is encased in a plywood box. His head protrudes through a hole in the top and great white clouds of fresh seawater steam curl out of the box and around his neck, like a frilly collar. His eyes are glazed. He looks like he's on drugs.

We are sharing a cubicle at Kilcullen's Seaweed Baths (kilcullenseaweedbaths.com) on the edge of Enniscrone beach in County Sligo, north-west Ireland. I'm in a huge, ancient cast iron bath with crackled cream enamel, and I've decided to float on my back in the green water, piling the huge mounds of luscious fleshy seaweed all over me. I float easily in this salty hot water, and, as I close my eyes and breathe through the steamy fronds, I, too, feel like I'm on drugs.

"Sure, there's no time limit," a red-haired freckled-faced teenager had told us as she showed Rex and me to our bedsit-sized cubicle. "If the bath water comes cold, there's plenty more hot in the tap."

She then showed us a wooden lever inside the box that, if pushed, would gush Industrial Revolution-sized clouds of seawater steam into the cabinet. She suggested we take it in turns: one in the bath, one in the steam box, until we are both perfectly blanched. Then, she suggested, we should scoop all the seaweed out of the bath, pile it into the bucket provided (we could easily have filled two buckets with all our steaming weed); let out our bathwater, and then take it in turns to stand under a fireman's hose-like shower of fresh cold seawater.

Lying in the bath I can feel a warm mucous slime beginning to cling to my skin. It's womb-like. Soft and velvety. Sensual. People with skin conditions; eczema and dermatitis, as well as sportsmen and women love these baths. Many of the local pensioners have season tickets ("To warm their old bones in the winters") and I'm told it is a very popular hangover cure. After the hot silky seaweed soak, the stinging, cleansing, pins-and-needles of the cold seawater shower leaves a bather feeling newly minted.

Kilcullen’s Seaweed Baths, which opened in 1912. Photograph: Alamy

The baths are housed inside a castle-like structure built in 1912, with flat roofs to hold the massive reservoirs that are filled twice a day with seawater pumped from Enniscrone bay. Standing outside, Rex and I lick honeycomb-flavoured ice-creams and stare across the massive billiard table-flat sandy beach towards America. There's no land between us and New York.

Actually, we're in Ireland for salmon. The river Moy, flowing from Loch Conn to the estuary at Ballina, is the most prolific salmon river in Ireland. And two miles of the middle Moy, in County Mayo, flows along the edge of the Mount Falcon hotel's 100 acres of lush wooded grounds.

My wife Helen and I and our four children are staying in a self-catering cottage overlooking the hotel's trout lake. Three of my children caught salmon on the first morning. The Moy is hoaching with fresh-run fish this season. Anglers have been enjoying a boom in salmon catches ever since the Irish government was finally persuaded, in 2007, to close down the commercial drift net fishery that captured thousands of Irish salmon on their return migration from feeding grounds around Greenland.

In our week of travelling around the west coast from Mayo up to Donegal, we fished rivers and lakes, swam in the sea, hiked across peat bogs, climbed "One man's path" up Slieve League, the 600m-high sea cliffs that fall in a sheer testicle-shrinking drop, to the white topped sea below. We drank Guinness, we rowed across a bay to a sheep-inhabited island no bigger than a football pitch where we barbecued mackerel and ate them with soda bread and horseradish sauce. We caught six salmon in total. We released two (hen fish are a precious resource) and cooked two. And we left two at Clarke's Salmon Smokery in Ballina, to be posted on to our home in Dorset.

The towering cliffs of Slieve League, Donegal

The things we enjoyed the most about Mayo were the things that haven't changed for decades, the sea, the sand, the salmon, the scenery and the people.

"Would you be wanting to take your seaweed home with you?" asks Ted, a biochemistry student from Galway University, who is working the summer holidays at Kilcullen's, which was opened by his great-grandfather 100 years ago.

My mouth opens and shuts like a fish. I don't quite know how to answer his question. He then explains that some people like to reuse their bucket of serrated wrack (Fucus serratus) in a bath back at home. The wrack is harvested by hand, by his cousins, from the beach at low tide every day of the year except Christmas day. Some people also like to take it home to spread on their garden as fertiliser.

Sadly, I have to decline this so delightful and very Irish offer. I just know Ryanair will have a small-print policy about seaweed in hand baggage. Sadly, too, there has in recent years been an erosion of this grounded and charming Irishness.

"A lot of fecking froth," says Alan Maloney, owner of the Mount Falcon. "Aw Jeez, there was an awful, awful lot of froth. Yep, we all got to look pretty stupid for a while back there."

Alan is, of course, referring to the Irish banking crisis and the fatal wounds inflicted on the once rampant Celtic Tiger economy. He had built a helipad in the grounds.

"Helicopters were buzzing in and out of here like bees," he remembers. "Businessmen from Dublin, flying up just for lunch. Americans buzzing from golf course to golf course."

Now, the helicopters have stopped buzzing. And tourists have dwindled as the euro crisis has deepened. And some of the froth just looks silly.

Not this, though. A 100-year-old hot sea water and seaweed bath experience costs €25 for one (€32 for two). A family suite of two huge baths and two steam boxes costs only €40 ("And you can have as many as you like in there," says Ted. "We had a whole hen party in one before now. Was mad.")

Elsewhere in Mayo, there are boutique "spa" hotels advertising caviar facials at €130, a "Rasayana eternity body booster" at €100 or a "half-hour exotic coconut and frangipani wrap/float" for €80.